A Cartan-Hartogs version of the Polydisk Theorem

TL;DR

This paper extends the Polydisk Theorem to Cartan-Hartogs domains, demonstrating inheritance of totally geodesic submanifolds and characterizing geodesics with linear support within these complex structures.

Contribution

It introduces a Cartan-Hartogs version of the Polydisk Theorem, expanding geometric understanding of these domains and their geodesic properties.

Findings

Cartan-Hartogs domains inherit totally geodesic submanifolds from symmetric bounded domains

Characterization of Cartan-Hartogs geodesics with linear support

Extension of the Polydisk Theorem to new domain classes

Abstract

We extend the Polydisk Theorem for symmetric bounded domains to Cartan-Hartogs domains, and apply it to prove that a Cartan-Hartogs domain inherits totally geodesic submanifolds from the bounded symmetric domain which is based on, and to give a characterization of Cartan-Hartogs's geodesics with linear support.